Barack Obama's former White House chief of staff, Rahm Emanuel, is within reach of winning outright in the Chicago mayoral election, according to polls.

If he fails to reach 50%, he will face a runoff on 5 April. The last poll put him tantalisingly close, on 49%.

He was cautious in a television interview on Monday, refusing to say whether he thought he could win without a runoff.

Emanuel, well-known for his brashness and his foul-mouthed rants, quit the White House last year to seek the top job in his native Chicago, which is solidly Democratic.

Rahm's chances of winning outright rose after an angry outburst by one of his challengers, Carol Moseley Braun, in a debate last month.

Moseley Braun, who had hoped she would win over most of the city's African-American vote, was angered by a comment by one of the marginal contestants, the community activist Patricia Van Pelt-Watkins, who said she had not heard much from Moseley Braun in the past seven years.

Moseley Braun responded in the no-holds-barred way for which the city is notorious: "Patricia, just because you didn't know who I was for the last seven years is because you were on crack." Van Pelt-Watkins has been drug-free for at least two decades.

A Chicago Tribune/WGN poll on 10 February – the last one to be published – put Emanuel on 49%, well clear of his nearest rival, Gery Chico, on 19%.

Chico, a lawyer and the former chief of staff to Richard Daley, the current mayor, has been courting the Hispanic vote.

Emanuel's sudden poll jump, which saw him win more support among African-Americans, followed Moseley Braun's outburst. Moseley Braun fell to 10%. Miguel del Valle, the city clerk, was on 8%.

The biggest threat to Emanuel was a court case challenging whether he was eligible to stand under residency rules.

His challengers questioned whether he had lived in the city long enough but he rejected the claim, and the courts kept his name on the ballot.

Although Emanuel was not formally backed by Obama, he won the endorsement in January of the former president Bill Clinton, who remains popular among Democrats.

Emanuel accumulated a campaign chest amounting to more than $11m (£6.7m), according to finances declared up until the end of December, compared with Chico's $2.5m.